MATHEMATICS COLLEGE

To make a specific shade of green paint, Timia mixes 2 cups of blue paint with 10 cups of yellow point. How many cups of yellow paint should she mix with one cup of blue paint to make the same shade of green.

Answers

Answer 1

Answer:

Answer:

1 cup of blue paint required 5 cups of yellow paints

Step-by-step explanation:

Given

2 cups of blue = 10 cups of yellow

Required

Determine the number of cups of yellow for 1 cup of blue paint

The given parameter shows a linear relationship between paints of blue and paints of yellow

We have:

2 cups of blue = 10 cups of yellow

Multiply both sides by 0.5

0.5* 2 cups of blue = 0.5* 10 cups of yellow

1 cup of blue = 5 cups of yellow

Hence;

1 cup of blue paint required 5 cups of yellow paints

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find the critical points and classify them as local maxima, local minima, saddle points, or none of these.

Answers

This question is incomplete, the complete question is;

find the critical points and classify them as local maxima, local minima, saddle points, or none of these.

f(x,y) = (x + y)(xy + 1)

Answer:

(x,y) = (-1, 1), (1, -1) area critical points

f(xx) =2y, fyy =2x,f(xy) =2x + 2y, D = f(xx)fyy - f(xy²)

at (-1, 1)

f(xx) = 2 ,fyy =-2,f(xy) = 0, D = -4 < 0 saddle point

at (1, -1)

f(xx) = -2, fyy =2,f(xy) =0, D = -4 < 0 saddle point

Step-by-step explanation:

Given that;

f(x,y) = (x + y)(xy + 1)

f(x,y) =x²y + xy² + x + y

for critical points fx =0 ,fy =0

fx = 2xy + y² + 1 = 0, fy = x² + 2xy + 1 = 0

2xy + y² + 1 = 0, x²+ 2xy + 1 = 0

2xy + y² + 1 - x² - 2xy - 1 = 0

x² = y²

=> x = y, x = -y

2xy + y² + 1 = 0, x = y

2yy + y² + 1 = 0

3y² = -1 , no solution

2xy + y² + 1 = 0, x = -y

-2yy + y² + 1 = 0

=> -y2 + 1 = 0

=> y = -1, y = 1

y = -1 => x = 1, y = 1 => x = -1

(x,y) = (-1, 1), (1, -1) area critical points

f(xx) =2y, fyy =2x,f(xy) =2x + 2y, D = f(xx)fyy - f(xy²)

at (-1, 1)

f(xx) = 2 ,fyy =-2,f(xy) = 0, D = -4 < 0 saddle point

at (1, -1)

f(xx) = -2, fyy =2,f(xy) =0, D = -4 < 0 saddle point

What is the length of AC?

Answers

The length of AC found using the Pythagorean Theorem is C) 120.

The length of AC can be found using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is AC, and the other two sides are AB and BC.

AB = 60 units

BC = 80 units

Plugging these values into the Pythagorean Theorem, we get:

$AC^2$ = $AB^2$ + $BC^2$